QD 


UC-NRLF 


7^7 


EXCHANGE 


THE  PRESSURE  EFFECT  IN  SELENIUM 

CRYSTALS  AND  ITS  RELATION 

TO  THE  LIGHT  EFFECT 


By 


ERNEST  OTTO  IDIETERICH 

A.B.,  University  oTTowa,  1912 
M.S.,  University  of  Iowa,  1914 


JUL  3 


THE  PRESSURE  EFFECT  IN  SELENIUM 

CRYSTALS  AND  ITS  RELATION 

TO  THE  LIGHT  EFFECT 


By 


ERNEST  OTTO  UIETEIUCH 
A.B.,  University  of  Iowa,  1912 
M.S.,  University  of  Iowa,  1914 


THESIS 

Submitted  in  partial  fulfillment  of  the  requirements  for  the  Degree  of  Doctor 

of  Philosophy  in  Physics,  in  the  Graduate  College  of  the 

State  ^University  of  Iowa,  June,  1916 


Iowa  City,  Iowa 


EXCHANGE 


THE  PRESSURE  EFFECT  IN  SELENIUM 

CRYSTALS  AND  ITS  RELATION  TO 

THE  LIGHT  EFFECT 

By  E.  O.  DIETERIOH 

ABSTRACT 

The  effect  of  pressure  on  selenium  crystals  is  shown  to  be  of  a  different 
nature  from  that  produced  by  light.  According  to  Brown  '&  theory  of  electric 
conduction  in  selenium,  the  change  of  resistance  produced  by  light  is  due  to 
a  change  in  the  rate  of  emission  of  electrons  from  the  atoms  during  illumin- 
ation, while  their  coefficient  of  recombination  is  unaffected  by  the  intensity  of 
illumination.  Tlus  assumption  is  here  verified  by  experiments.  In  the  case  of 
pressure,  however,  these  experiments  show  that  the  coefficient  of  recombination 
is  the  factor  that  is  altered,  and  the  greater  the  pressure  the  smaller  is  the 
coefficient  of  recombination.  A  consideration  of  the  various  agencies  capable 
of  changing  the  conductivity  of  selenium,  such  as  light,  pressure,  temperature 
and  potential  gradient,  leads  to  the  conclusion  that  the  only  one  which  modifies 
the  rate  of  emission  of  conducting  electrons  is  light,  the  others  affecting  only 
the  coefficient  of  recombination. 

INTRODUCTION 

The  discovery1  of  a  method  of  producing  large  crystals  of  sele- 
nium provided  additional  means  for  the  study  of  the  interesting 
optical  and  electrical  properties  of  this  element  in  the  crystalline 
or  metallic  modification.  As  a  result  of  the  investigation  of  some 
of  these  properties,  Brown2  has  proposed  an  explanation  of  the 
nature  of  the  electrical  conductivity  of  selenium.  According  to 
this  theory,  which  is  essentially  of  the  same  nature  as  J.  J.  Thom- 
son's doublet  theory  of  electrical  conduction  in  metals,  the  con- 
ductivity of  selenium  may  be  altered  in  two  ways,  either  by  a  change 
in  the  rate  of  liberation  of  conducting  electrons  from  the  atoms,  or 
by  a  change  in  the  rate  of  recombination  of  the  electrons  with  the 
atoms.  These  assumptions  were  verified  in  certain  experiments3  in 
which  the  effect  of  light  in  changing  the  conductivity  of  selenium 
crystals  under  various  conditions  of  temperature,  pressure  and 
potential  gradient  were  studied. 

Since  a  change  in  pressure  produces  such  a  marked  effect  on  the 


iF.  C.  Brown,  Phys.  Rev.,  4,  85,  (1915). 

zF.  C.  Brown,  Phys.  Rev.,  5,  395,  (1915). 

s  P.  C.  Brown,  Phys.  Rev.,  5,  395,  (1915)  and  Phys.  Rev.,  7,  551,  (1916). 


B74678 


resistance  of  selenium  it  is  of  importance  to  investigate  the  pressure 
effect  in  more  detail,  in  order  to  test  the  theory  more  completely 
in  that  direction.  The  experiments  described  below  were  so  ar- 
ranged that  the  changes  of  conductivity  produced  by  pressure 
changes  could  be  studied  immediately  after  the  variation  in  pres- 
sure. 

THEORY 

Assuming  that  the  conductivity  of  a  selenium  crystal  at  any 
instant  is  directly  proportional  to  the  number  of  conducting  elec- 
trons present,  it  has  been  shown4  that  when  the  equilibrium  con- 
ditions have  been  disturbed,  the  rate  of  change  of  conductivity 
may  be  expressed  by 

di/dt  =  —  a  i2 (1) 

Here  i  represents  the  equilibrium  conductivity  of  a  crystal  under 
fixed  conditions  of  light  intensity,  temperature,  pressure  and  poten- 
tial gradient,  and  a  is  the  coefficient  of  recombination  of  the  con- 
ducting electrons  with  the  atoms. 
Equation  (1)  was  tested  in  the  form 

Ai/At •=  —  a  i2. 

by  a  series  of  experiments  in  which  the  equilibrium  value  of  the 
conductivity  was  altered  by  a  change  in  the  light  intensity.  Ai 

At 

was  measured  directly  (At  being  .02  sec.)  and  a  calculated.    For 
light  intensities  over  a  wide  range  a  was  found  constant,  justifying 
the  assumption  made  that  a  is  independent  of  light  intensity  and 
has  the  same  value  in  the  dark  as  in  the  light. 
At  equilibrium,  in  the  dark, 

di/dt  =  —  a  i02  (2) 

Writing  q  for  the  rate  of  emission  of  conducting  electrons  in  the 
dark,  and  M  for  the  increase  in  the  rate  of  emission  due  to  light, 
we  have,  at  equilibrium  in  light  of  constant  intensity, 

di/dt  ==  —  a  i^  =  M  +  q (3) 

in  which  iL  is  the  equilibrium  conductivity  in  the  light. 
From  the  above  equation  we  obtain 


i1==          ^ (4) 


C.  Brown,  Phys.  Rev.,  5,  395,  (1915). 


which  shows  that  a  change  in  conductivity  may  be  produced  by 
varying  either  M  or  a.  The  constancy  of  a  in  light  of  various  wide- 
ly different  intensities  shows  that  M  is  the  quantity  modified  by 
exposure  to  light. 

Similarly,  if  it  be  assumed  that  change  of  pressure  alters  the  rate 
of  emission  of  electrons  in  the  same  manner  that  change  of  illumin- 
ation does,  we  may  write  M ^  for  the  increase  due  to  pressure  alone, 
and  obtain 


(5) 


The  constants  in  Eq.  (5)  may  be  determined  by  the  same  method 
employed  for  Eq.  (4),  the  change  in  conductivity  being  produced 
by  a  variation  in  the  pressure  upon  the  crystal.  If  the  pressure 
and  light  effect  are  the  same  c^  will  remain  constant  for  different 
pressures. 

EXPERIMENTAL  ARRANGEMENTS  AND  METHOD 
OF  MEASUREMENTS 

The  crystal  under  observation  was  held  horizontally  between 
platinum  electrodes  in  one  arm  of  a  Wheatstone  bridge.  A  weight 
of  500  grams,  L,  rigidly  fixed  to  a  hinged  rod  rested  upon  the  upper 
electrode.  This  weight  was  connected  to  a  shaft  of  a  heavy  timing 
pendulum  by  means  of  a  cord  passing  over  a  pulley  system.  The 
pendulum  served  as  a  means  of  raising  L  at  the  instant  of  closing 
the  key  in  the  galvanometer  circuit.  A  second  key  was  also  tripped 
by  the  pendulum  and  opened  the  circuit  at  the  end  of  a  pre-deter- 
mined  short  time  interval,  in  these  experiments,  .04  sec.  Different 
constant  pressures  were  obtained  by  suspending  weights  W  from 
a  long  shanked  hook  attached  to  the  upper  electrode  and  passing 
through  a  hole  in  the  base.  These  weights  were  so  chosen  that  the 
pressure  upon  the  crystal  ranged  from  10  kg/cm2  to  100  kg/cm2. 
At  pressure  higher  than  the  latter  the  crystal  resistance  became  too 
unsteady  to  obtain  reliable  readings.  The  electrodes  and  weights 
were  enclosed  in  a  light  tight  box  provided  with  a  slit  directly  in 
front  of  the  crystal,  which  was  opened  when  the  light  effects  were 
studied.  A  Nemst  glower,  at  a  distance  of  75  cm.  from  the  crystal, 
was  used,  and  the  time  of  exposure  of  the  crystal  to  light  was  regu- 
lated by  means  of  a  shutter  attached  to  the  timing  pendulum. 

The  method  of  Brown  and  Clark5  for  measuring  rapid  fluctua- 

5  F.  C.  Brown  and  W.  H.  Clark,  Phys.  Rev.,  32,  251,  (1911)  and  Phys.  Rev., 
33,  53,  (1911). 


tions  in  resistance  was  slightly  modified  to  obtain  the  change  of 
resistance  of  the  crystal  during  the  .04  sec.  following  a  change  in 
the  equilibrium  conditions.  All  factors  besides  light  intensity  and 
pressure  were  kept  constant.  Readings  were  made  at  room  tem- 
perature which  was  maintained  constant  to  a  few  degrees  centi- 
grade. The  potential  drop  across  the  crystal  was  at  all  times  14.2 
volts,  and  since  the  crystals  were  all  of  approximately  the  same  size 
the  potential  gradient  may  be  assumed  constant.  A  large  number 
of  crystals  of  several  types  was  studied  and  satisfactory  duplication 
of  data  obtained.  For  purposes  of  comparison  the  results  given 
below  were  all  chosen  from  the  data  referring  to  a  single  crystal 
which  was  a  large  hexagonal  specimen  about  1  mm.  thick  and  5 
mm.  long. 

RESULTS 

The  Pressure  Effect  in  the  Dark  and  under  Constant  Illumination 
The  crystal  was  allowed  to  reach  equilibrium  in  the  dark  under 
the  pressure  due  to  W  -f-  L.  Its  recovery  in  the  first  .04  sec.  im- 
mediately following  a  change  in  the  pressure  due  to  the  removal 
of  L  was  determined  for  different  values  of  W.  This  procedure 
was  followed  rather  than  that  of  changing  the  conditions  by  the 
addition  of  L  because  of  the  danger  of  crushing  the  crystal  con- 
tinuously exposed  to  light  of  constant  intensity.  Table  I,  below, 
summarizes  the  data. 

TABLE  I 

PRESSURE  EFFECT  ON  CONDUCTIVITY 
L  =  500  grams;  i0  =  initial  conductivity;  ij  =  conductivity  after  .04  sec. 


W 

(X10T) 

i, 

(X107) 

Crystal 

Ai 

(X10T) 

in  the  Dark 

(xlO-r) 

oM 

(X10T) 

500  gm. 
1000    " 
2000    '" 
3000    » 

6.71 
8.55 
11.86 
15.79 

4.23 
6.91 
10.97 
15.00 

2.48 
1.64 
.89 
.79 

1.37 
.560 
.158 
.079 

92.2 
41.1 

22.2 
19.8 

500  gm. 
1000    " 
2000    " 
3000    " 

20.00 
24.90 
34.10 
44.00 

Crystal 
12.26 
19.40 
31.26 
41.20 

in  the  Light 
7.74 
5.50 
2.84 
2.80 

.486 
.222 
.061 
.036 

194.1 
137.7 
71.0 
69.8 

Column  5  of  the  table  shows  the  decrease  of  a  with  increasing 
pressure,  the  rate  of  decrease  being  a  little  greater  in  the  light  than 
in  the  dark  when  the  factor  by  which  the  conductivity  is  altered 
by  pressure  is  the  same.  In  the  next  column  are  tabulated  the  varia- 


tiou  of  cd02  with  pressure,  the  value  of  <xi02  showing  a  decided  de- 
crease. Now,  from  Eq.  (4)  it  is  evident  that  a  change  in  i  may  be 
the  result  of  either  a  change  in  a  or  a  change  in  M  -f-  3>  the  rate  of 
emission  of  conducting  electrons.  These  experiments  show  that 
part  of  the  change,  at  least,  is  due  to  a  change  in  a ;  the  variation 
in  a  is  not  sufficient  to  warrant  the  conclusion  that  the  only  effect 
of  pressure  is  to  vary  the  rate  of  recombination,  and  not  the  rate 
of  emission.  But  considered  in  connection  with  the  decrease  in 
ai02  and  with  experiments  to  be  described  in  the  next  section,  it 
may  be  concluded  that  such  is  actually  the  case. 

The  Light  Effect  at  Different  Pressures,  Intensity  of 

Illumination  Constant 

In  these  experiments,  after  equilibrium  conductivity  had  been 
reached  in  the  light  the  intensity  was  reduced  by  a  constant  amount, 
by  means  of  a  darkened  photographic  plate,  and  the  rate  of  re- 
covery measured  for  different  values  of  W.  The  values  for  a  and 
for  ai02  can  then  be  compared  with  those  determined  for  a  constant 
change  of  pressure  above. 

TABLE  II 
LIGHT  EFFECT  AS  A  FUNCTION  OF  PRESSURE 


W 

(X10T) 

(XiV) 

Ai 

(X10T) 

(xlO-r) 

aio 

(X10°T) 

500  gm. 
1000    J> 
2000    " 
3000    » 
4000    » 

15.36 
19.20 
28.47 
38.15 
47.35 

14.36 
18.05 
28.70 
35.90 
44.40 

1.00 
1.15 
1.77 
2.25 
2.95 

.106 
.078 
.054 
.039 
.033 

1.62 
1.50 
1.50 
1.47 
1.57 

25.00 
28.75 
43.75 
56.40 
74.00 

Table  II  represents  the  results  obtained,  a  decrease  in  a  but  an 
increase  in  aiu2  showing  quite  clearly  that  the  action  of  pressure 
and  light  in  producing  a  conductivity  change  are  different.  The 
pressure  effect  is  shown  in  the  decreasing  value  for  a,  the  light 
effect,  in  the  increasing  values  for  od02  (See  equation  4). 

The  Light  Effect  at  Constant  Pressure,  Intensity  of 

Illumination  Varied 

Table  III  summarizes  the  results  obtained,  agreeing  with  those 
determined  by  previous  work8  and  the  constancy  of  a  again  points 
to  the  change  in  the  rate  of  emission  of  electrons  under  the  influence 
of  illumination. 


.  C.  Brown,  Phys.  Rev.,  5,  395,  (1915). 


TABLE  III 


Intensity 

W 

(X10T) 

(XIO*) 

Ai 
(xlOT) 

a 
(xlO-7) 

aio2 
(x!07) 

1 

2 
3 

1000  gm. 
1000    " 
1000    » 

32.00 
26.10 
19.74 

30.75 
25.20 
19.29 

1.25 
.90 
.45 

.031 
.033 
.029 

31.9 
22.6 
11.2 

The  Effect  of  a  Simultaneous  Change  in  Pressure  and  Light  In- 
tensity is  shown  in  Table  IV,  and  indicates  the  dissimilarity  in  the 
action  of  light  and  pressure. 


TABLE  IV 


W  =  500  grams. 
L    =  500  grams. 

(XlOT) 

(XlOT) 

Ai 

(XlOT) 

a 

(XIO'T) 

(xYoT) 

Light 
Pressure 
Light  &  pressure 

13.34 
8.97 
20.81 

12.72 
7.86 
15.58 

.62 
1.11 
5.23 

.09 
.34 

.30 

15.4 

27.8 
131.0 

The  values  of  a  due  to  a  change  in  pressure,  and  to  a  change  in 
both  light  and  pressure  are  practically  the  same,  showing  that  the 
change  in  conductivity  produced  by  the  action  of  light  is  caused  by 
a  change  in  the  rate  of  emission  of  electrons  by  the  atoms.  The 
behavior  of  the  crystals  in  these  experiments  is  worthy  of  note. 
When  they  were  kept  in  the  dark,  and  the  conductivity  altered  by 
a  change  in  pressure,  they  rapidly  recovered  their  initial  conduc- 
tivity on  the  restoration  of  original  conditions,  the  recovery  from 
the  light  effect  was  somewhat  slower,  a  matter  of  a  quarter  of  an 
hour,  but  the  return  to  equilibrium  conditions  when  disturbed  by 
both  light  and  pressure  was  very  slow — frequently  several  hours 
were  required  before  the  initial  conductivity  had  been  reached. 

CONCLUSIONS 

In  all  the  results  discussed  above  the  same  fact  is  evident,  that 
is,  that  the  effect  of  pressure  is  merely  to  decrease  the  coefficient 
of  recombination  of  the  conducting  electrons  with  the  positive  resi- 
dues of  the  atoms  from  which  they  have  escaped.  In  no  case  can 
the  experimental  results  be  taken  to  indicate  an  increased  rate  of 
emission  of  electrons,  for  with  increasing  pressure,  a  decreasing 
value  of  a  was  always  observed.  Now,  Brown7  has  shown  that  with 
an  increase  in  the  potential  drop  across  a  crystal  the  value  of  a  due 
to  a  change  in  the  light  intensity  is  decreased  in  the  same  manner 


7  Loc.  dt. 


as  it  is  in  the  case  of  pressure.  Further  Mrs.  Dieterich8  showed  that 
the  temperature  effect  on  a  is  similar  to  that  observed  in  the  case 
of  pressure  and  voltage.  The  conclusion  is  obvious — the  only  agency 
which  changes  the  conductivity  of  selenium  by  causing  an  increase 
in  the  rate  of  emission  of  conducting  electrons  is  light ;  pressure, 
temperature  and  potential  difference  affect  the  coefficient  of  recom- 
bination of  the  conducting  electrons  with  the  atoms. 


K.  J.  Dieterich,  Phys.  Rev.  2,  Vol.  VII,  p.  551,  (1916). 


G74678 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


